For these reasons, it suffices to bound the risk \(\mathcal {R}(\hat{\theta }^{d}_{n, V}, \theta ^{*})\)  under the assumption \(V_2(\theta ^{*}) \le V\) .
We exploit the following general result of convex-constrained least squares estimators to bound this risk.
Theorem REF  is essentially from [1]}, and one can refer to [2]} to see how the results of [1]} yield Theorem REF .
Note that since \(C(V)\)  is closed and convex, \(\hat{\theta }^{d}_{n, V}\)  is basically a convex-constrained least squares estimator of \(\theta ^{*}\) .
